Is the periodic sum of y = sin (x + 3 π / 4) + cos (x + 3 π /) an odd function or an even function?

Is the periodic sum of y = sin (x + 3 π / 4) + cos (x + 3 π /) an odd function or an even function?

Is y = sin (x + 3 π / 4) + cos (x + 3 π / 4)?
y=√2sin(x+3π/4+π/4)=√2sin(x+π)=-√2sinx
Period is 2 π, odd function

Is y = sin (PAI / 4 + x) cos (PAI / 4 + x) an odd function or an even function? What is the cycle?

y=1/2*[2sin(π/4+x)cos(π/4+x)]
=1/2*sin[2(π/4+x)]
=1/2*sin(π/2+2x)
=1/2*cos2x
So this is an even function
T=2π/2=π

F (x) = sin (n π - x) cos (n π + x) / cos ((n + 1) π - x) * Tan (x-n π) * cot (n π / 2 + x), find the value of F (π / 6)

When n is even f (x) = sin (n π - x) cos (n π + x) / cos ((n + 1) π - x) * Tan (x-n π) * cot (n π / 2 + x) = sin (- x) cosx / [- cos (- x)] tanxcotx = SiNx = sin π / 6 = 1 / 2 when n is odd f (x) = sin (n π - x) cos (n π + x) / cos ((n + 1) π - x) * Tan (x-n π) * cot (n π / 2 + x) = [- sin

If f (x) = {sin (n-pie-x) cos (n-pie + x) / cos [(n + 1) pie-x]} * Tan (x-n-pie) cot [(n-pie / 2) + x], n belongs to Z, find the value of F (7 Pie / 6)

F (x) = {sin (n-pie-x) cos (n-pie + x) / cos [(n + 1) pie-x]} * Tan (x-n-pie) cot [(n-pie / 2) + x]
={sin (- x) cosx / cos [(n + 1) pai-x]} * TaNx * cot [(n Pai / 2) + x]
If n is odd,
F (x) = {sin (- x) cos (x) / cos [(n + 1) pai-x]} * tanxcot [(n Pai / 2) + x]
={sin (- x) cosx / cosx} * TaNx * cot [(Pie / 2) + x]
=-sinx*tanx*(-tanx)
=sinx*(tanx)^2
F (7 pies / 6) = - 1 / 6
If n is even,
F (x) = {sin (- x) cos (x) / cos [(n + 1) pai-x]} * tanxcot [(n Pai / 2) + x]
={sin(-x)cosx/(-cosx)}*tanx*cotx
=sinx
F (7 pies / 6) = - 1 / 2

f(x)=sin(nπ-x)cos(nπ+x)\cos[(n+1)π-x]*tan(x-nπ)cot(nπ+x) N ∈ Z, find the value of F (π \ 6) I can't figure it out f(x)={[sin(nπ-x)cos(nπ+x)]\cos[(n+1)π-x]}*tan(x-nπ)cot(nπ+x) The title should be like this.

If n is odd, f (x) = - SiNx. If n is even, it is SiNx, which can be substituted

Let f (x) = [sin (3 π - x) cos (x - π) Tan (x - π) cot (n π / 2 + x)] / cos (n π - x), (n ∈ z) (1) find f (52 π / 3) (2) F (x) = [sin (3 π - x) cos (x - π) Tan (x - π) cot (n π / 2 + x)] / cos (n π - x), (n ∈ z) (1) Find f (52 π / 3) (2) If cos（ α- 3 π / 2) = 4 / 5, find F（ α) Value of

1, n is even, = 3 / 4; N is odd, = 3, radical 3 / 4
2, n is even, = 4 / 25; N is odd, = plus or minus 16 / 75